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equatorial coordinate system

 
 
Columbia Encyclopedia: equatorial coordinate system
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equatorial coordinate system, the most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere. The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox, the point at which the sun crosses the celestial equator in March.

To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle, analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0h and declination 0°.

Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time. The angular distance from the sigma point to a star's hour circle is called its hour angle; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.

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Wikipedia: Equatorial coordinate system
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The spherical coordinate system

The Equatorial Coordinate System is a popular method of mapping celestial objects. It functions by projecting the Earth's geographic poles, equator, and ecliptic onto the celestial sphere. This allows stars to be cataloged by objective locations (as opposed to the horizontal coordinate system, commonly known as an altitude-azimuth or azimuth-elevation system, in which stars' coordinates are dependent on the observer's location on Earth). The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, the projections of the Earth's North and South geographic poles become the North and South celestial poles, respectively.

There are two systems to specify the longitudinal (longitude-like) coordinate:

  • the hour angle system is fixed to the Earth like the geographic coordinate system
  • the right ascension system is fixed to the stars, thus, during a night or a few nights, it appears to move across the sky as the Earth spins and orbits under the fixed stars. Over long periods of time, precession and nutation effects alter the earth's orbit and thus the apparent location of the stars. When considering observations separated by long intervals, it is necessary to specify an epoch (frequently J2000.0, for older data B1950.0) when specifying coordinates of planets, stars, galaxies, etc.
Left A star is at culmination on an observer's meridian (HA = 0 h), then RA = LST. Right Now the vernal equinox point is at culmination on the meridian m (LST = 0 h) (Positive angles: RA, counterclockwise; HA and LST, clockwise)

The latitudinal (latitude-like) angle of the equatorial system is called declination (Dec for short). It measures the angle of an object above or below the celestial equator. The longitudinal angle is called the right ascension (RA for short). It measures the angle of an object east of the vernal equinox point. Unlike longitude, right ascension is usually measured in hours instead of degrees, because the apparent rotation of the equatorial coordinate system is closely related to sidereal time and hour angle. Since a full rotation of the sky takes 24 hours of sidereal time to complete, there are (360 degrees / 24 hours) = 15 degrees in one hour of right ascension.

The equatorial coordinate system is commonly used by telescopes equipped with equatorial mounts by employing Setting circles. Setting circles in conjunction with a star chart or ephemeris allow a telescope to be easily pointed at known objects on the celestial sphere.

GEI Coordinates

There are a number of cartesian variants of equatorial coordinates. The most common of which is called Geocentric Equatorial Inertial(GEI) coordinates.

  • GEI coordinates have the Z-axis pointing along the axis of rotation of the earth (North positive), the X-axis pointing in the direction of the Sun during the Vernal Equinox and the Y-axis defined as the cross product of Z and X (in that order) to create a right handed coordinate system. Like the polar variants described above, the direction of the X-axis drifts due to orbital precession and thus an epoch must be specified.
  • In this context, J2000.0 can also refer not just to the Julian 2000 Epoch, but also to the entire GEI coordinate frame at that epoch.
  • GEI systems are also sometimes "True of Date". This means that the epoch at the exact moment at which the data is collected is used as the epoch of the coordinate system.
  • The direction of the X-axis is also described as the first point of the constellation Aries.
  • This system is often used for describing the state vectors of spacecraft as well as various phenomena in space physics.[1][2][3]

See also

  1. ^ Geocentric coordinate systems, http://sspg1.bnsc.rl.ac.uk/Share/Coordinates/geo_sys.htm 
  2. ^ Space physics coordinate systems, http://www.iki.rssi.ru/vprokhor/coords.htm 
  3. ^ Christopher T. Russell, Geophysical Coordinate Transformations, http://dawn.ucla.edu/personnel/russell/papers/gct1.html/ 

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